A sonic-logging tool called a sonde is commonly lowered into wellbores to generate and detect acoustic waves from which useful information is derived. A series of wave arrivals is detected by the tool after pulse initiation. The arrival times are proportional to the inverse of the wave velocity. The first arrival usually results from P-waves traveling in the formation penetrated by the wellbore. A P-wave is a longitudinal or compression wave, particle motion being in the direction of wave propagation. A second arrival in a typical sonic log is sometimes identified as S-wave travel in the formation. (Sheriff, Encyclopedic Dictionary of Exploration Geophysics, Society of Exploration Geophysicists (4th Ed., 2002)) An S-wave, or shear wave, has particle motion perpendicular to the direction of propagation. Following the S-wave is the Stoneley wave, a name given to surface waves in a borehole. In slow or soft formations where there is no S-wave, the Stoneley wave will be the second arrival in the sonic log. In general, Stoneley waves exhibit high amplitude and low frequency. Stoneley waves are usually distinct and readily identifiable arrivals in a sonic log.
The idea of using the Stoneley wave to predict reservoir permeability was proposed many years ago and thought to be a promising approach (Burns and Cheng, 1986; Cheng, et al., 1987). Stoneley wave measurements are the only data derived from sonic logs that are sensitive to permeability. P and S-waves are insensitive to permeability of the media through which they propagate. However, the applications of the existing Stoneley-wave permeability methods have had practicality issues. Their shortcomings include: 1) the inversion models are less sensitive to formation permeability; 2) practically, mud velocity is known only with large uncertainty, which can totally alter the relationship between Stoneley-wave velocity and permeability; 3) the effect of a mud cake on Stoneley-wave velocity cannot be separated from the effect of permeability, and a simultaneous multi-parameter inversion (permeability and mud cake property) will be non-unique; and 4) the use of either a low-frequency approximation or a simplified model is limited to low-frequency (˜1 kHz) Stoneley-wave measurements, while in most cases Stoneley wave energy is located at 1-5 kHz or even higher. Mud refers to an aqueous suspension called drilling mud pumped down through the drill pipe and up through the annular space between it and the walls of the wellbore in rotary drilling operations. The mud helps remove drill cuttings, prevent caving, seal off porous zones and hold back formation fluids. The mud cake is the mud residue deposited on the borehole wall as the mud loses moisture into porous, permeable formations. The mud cake retards further loss of moisture to the formation and thus tends to stabilize in thickness.
There appears to be no existing tool for readily measuring mud velocity, nor is there a standard approach disclosed in the literature for estimating mud velocity. Instead, a value of mud velocity is typically taken as known. While such assumed values may be close to actual, it is a finding of the present invention that even an uncertainty of 2%-3% in mud velocity may dramatically affect estimates of permeability based on Stoneley wave velocity or Stoneley wave amplitude, which are two currently used commercial techniques. The presence of a mud cake is a problem because it introduces further uncertainty in the mud velocity estimate and, in turn, in the deduced value of permeability. Some existing theories assume a hydraulic exchange between borehole fluid and formation pore fluid, an assumption that is negatively impacted by presence of a mudcake.
There have been a number of Stoneley-wave permeability methods developed. Hornby (1989) patented a method for determining the permeability using Stoneley-wave slowness (reciprocal of velocity). The slowness of a hypothetical Stoneley wave traveling in an elastic, non-permeable medium was computed based on an elastic borehole model. The computed Stoneley-wave slowness was subtracted from the measured Stoneley-wave slowness. The difference was used to determine formation permeability. The fundamental problems to this method are the limited change of Stoneley-wave slowness as a function of permeability change and the need of accurate mud velocity estimation, especially the latter factor because an error of 1% in mud velocity can lead to a permeability prediction error of up to 200%. Moreover, there is no single sonic tool designed to measure mud velocity in-situ, and hence, mud velocity cannot be estimated accurately in practice.
U.S. Pat. No. 4,964,101 to Liu et al. discloses a similar method. The difference is that the inversion model includes a mud cake compensated parameter to correct the measured Stoneley-wave slowness. The compensated parameter has an equivalent effect on Stoneley-wave slowness as permeability. However, such a compensated parameter cannot be measured and must be included in the inversion model as an unknown as well. Determining two unknowns simultaneously from a single Stoneley-wave slowness measurement will certainly yield non-uniqueness.
Tang et al. (1998) developed a method using Stoneley-wave central time shift and the corresponding wave central frequency shift to determine formation permeability. Generally, an attenuation of 1/QST will cause a shift of wave central frequency down to lower frequency. Such a central frequency shift is due to the total attenuation but not uniquely related to the attenuation due to formation permeability. The attenuation (1/QST) due to formation permeability is independent of the propagation distance. The central frequency shift is propagation distance dependent. Moreover, wave central frequency is closely related to the spectrum of the transducer. An exact estimation of wave central frequency shift can only be possible when the spectrum of the source is exactly known. Otherwise, the calculated wave central frequency shift will not correlate with permeability.
The existing published Stoneley-wave permeability methods mainly use Stoneley-wave slowness. These methods are known to suffer from low sensitivity to permeability and the effect of large uncertainty in mud velocity estimation. Those are the major reasons why the Stoneley-wave velocity permeability techniques have enjoyed limited success.
No published work has been found that discloses directly using Stoneley-wave attenuation (1/QST) to determine permeability. Cassell, et al. (1994) presents a method of using Stoneley-wave attenuation to predict formation permeability for carbonate based on an empirical relationship between Stoneley-wave attenuation and permeability. Chin (2001) developed a method using the total waveform energy (attenuation-related) to predict permeability based on an empirical relationship between waveform energy and permeability. Tang and Cheng (1996) developed a method of using Stoneley-wave amplitude to predict permeability based on the simplified Biot-Rosenbaum model.
For the foregoing reasons, there is a need for a more accurate permeability estimation, in particular, for the frequent cases where the mud velocity cannot be estimated accurately. The present invention satisfies this need by providing a method for directly using frequency-dependent Stoneley-wave attenuation 1/QST with full Biot theory, instead of simplified versions of the theory, to determine permeability. Biot theory describes seismic wave propagation in porous media consisting of solid skeleton and pore fluid (gas, oil, or water) and allows geophysicists to directly relate the seismic wave field to formation permeability.